A detached-eddy simulation (DES) model is proposed based on a fully hydrodynamic pressure model instead of hydrostatic model. The numerical scheme is based on finite volume method (FVM) on unstructured grids in the horizontal plane, and σ coordinate in vertical direction to fix free surface and uneven bottom. The in-house codes are paralleled using OpenMP. The proposed model is shown particularly effective in prediction of small-scale vortical structures.

Homoclinie intemections are soul.ce of chaos for a map.It is convenient to determine whether a given map iS chaotic or not by computing stable and unstable manifolds of its hyperbolic fixed point and observing if there are homoclinic intersections.A new algorithm is presented to compute one-dimensional stable and unstable manifolds of a map.Inspired by a unique property that derivative is transported along the orbit of one-dimensional manifold.position of new point is located quickly with a two-step "prediction and correction" scheme.Tangent component of the manifold is used as reference line to check if the uew point is acceptable.Performance of the algorithm is demonstrated with several typical chaotic maps.It shows that the algorithm is capable of computing both one- dimensional stable and unstable manifolds of maps.

In order to balance growth rate of manifold in all directions and construct global manifold structure of a dynamical system,a radial control factor is adopted to normalize the original dynamical system.Taking radius component of the tangent vector as a standard,this method controls manifold expanding at same speed in all directions.Theoretical analysis and example calculation demonstrate that manifolds before and after normalization have same orbit with the original one,which means their global manifold structures are consistent.Lorenz and Duffing systems are taken for examples to demonstrate effectiveness of the proposed approach.It indicates that the method not only get same effect as geodesic process but also present manifold in discrete flow way,which avoids many complicated boundary value problems.

With definition of DHT(distinguished hyperbolic trajectory) and existing measure function in phase space,a measure function in extended phase space is presented.Existing algorithms with constant accuracy parameters is laborious as high precision is required.In order to overcome this shortage,a variable-step convergence algorithm is proposed.The main idea is to estimate initial region with the help of ISP(instantaneous stagnation points) and adopt variable-step grids to increase efficiency.With theoretical analysis and numerical calculation,an optimal range of key parameter is given.Two-dimensional and three-dimensional Duffing systems are used to test the performance.It shows that convergence route gained by the developed measure function is smooth and stable.And the variable-step convergence algorithm is more efficient.

With embedding theorem proposed by Takens,we study methods for choosing proper delay time in phase space reconstruction of chaotic time series.A united method to incorporate advantages of average displacement and mutual information is put forward.In mutual information calculation we employ binary tree coding to divide and mark grids which makes it implemented easily.We determine layer numbers according to percentages of sparse grid.Numerical experiments of R ssler and Lorenz systems verifies accaracy of the method.

A scalable parallel algorithm especially for large-scale three dimensional simulations with seriously non-uniform molecular distributions is presented. In particular, based on cell-block data structures, this algorithm uses space filling curve to convert three-dimensional domain decomposition for load distribution across processors into one-dimensional load balancing problems for which run-time measurement-based multilevel averaging weights method can be applied successfully. Parallel numerical experiments for simulations of three-dimensional metal-eject physical models with 210 million particles using 500 processors of one massively parallel processors have shown that this algorithm has achieved speedup about 420.

Monte Carlo simulations are adopted to study the distribution of the nonlinear electric field in the reaction field of diamond film growth at low temperature via EACVD. The results indicate that the distribution of the electric field near the anode in the reaction field changes by exponential rules. Under certain bias voltages with the changing of pressure, there will be a reverse electric field near the anode. This reverse electric field is very important to some positive ions in diamond film growth at low temperature.

A spectral method in which wavelets are used as the basis functions is developed for solving acoustic and coupled structural-acoustic problems.On the basis of axisymmetric boundary integral formulation for axisymmetric bodies with arbitrary boundary conditions,the boundary quantities are expanded in wavelet series along the generator of the body,and a wavelet spectral formulation for solving acoustic problems of axisymmetric bodies is derived.Then, coupled wavelet spectral and finite element method is formulated for solving sound-structure interaction of axisymmetric elastic bodies with arbitrary boundary conditions.In this coupled method,a three-dimensional formulation is reduced to a one-dimensional one along the generator of the body.The coupled system is solved using the superposition principle for all the terms of Fouries series.The analysis of a submerged structure is performed.The comparisons of results based on the new technique with coupled finite element and boundary element methods are presented.Numerical solutions are given which show the fast convergence and the high accuracy.

Computation of three dimensional fluid interface instability with random perturbation is performed on a 8 CPU personal parallel computer system.The parallel computation platform is a message passage interface (MPI).A second order TVD scheme with Ghost method is applied with a fully parallel algorithm to the 3D Euler equations.Level Set function is used to track the motion of a fluid interface in an Eulerian framework.Buffer zone and data communication are discussed.The number of computation meshes is about 1 million.Bubble evolution with random perturbation in Rayleigh Taylor instability is obtained by numerical simulation.

It uses a Level Set function to track the motion of a fluid interface in an Eulerian framework.In addition,the use of Ghost cells (actually Ghost nodes in the difference framework) can keep the density profile from smearing out,while still preserving the scheme robust 2-nd easy to program with and accuracy TVD scheme in spacial and two step Runge Kutta methods.In contrast, the references[6][7] allow the density profile smearing out.This method significantly improves the resolution at the contact discontinuity.

On the basis of the message passing parallel programming platform MPI,and with the high performance characteristics of contemporary microprocessors,it describes the parallelization and optimization for a two dimensional molecular dynamics code(MDP) to simulate the high speed collision physical model problems.The serial optimization has shown to be of double performance improvements,and the parallel efficiencies being above 90% under the cluster consisted of 8 Pentium-Ⅱ microprocessors.

Recovery by equilibrium in patches (REP) technique is adopted for the non-linear transient heat conduction adaptive FEM analysis of casting system, which takes account of thermal conductivity of the interface. In order to test the present program, ANSYS and superconvergent patch recovery (SPR) methods are also employed for analysing the same problem respectively. The results of numerical analysis are compared with the experiment results, which show that REP method is cost effective.

The UTA method to calculate radiative opacity is outlined.Some results of Ge and Al are calculated and comparisons with experiments are given.

The shock compression of condensed matter can be effe ctively dealt with by molecular dynamics,and has been applied to many fields of science.However,there is large scale computation in molecular dynamics,so it is very important to develop the parallel and optimizing algorithm.An approach to the parallelization and optimization is proposed on the NOW (Network of Workstation),and has got the satisfactory result.

The RKDG method, proposed by Cockburn & Shu (1988), is developed into solution of N-S equation, and the results are compared with exact solution of Burger equation with viscousity. The result of 2D problem has been also compared with the one obtained by solving Euler equation.

A method is proposed for controlling partial differential equation directly to beam.It takes differential quadrature method in space domain and series in time domain,and yields equations of determining all parameters for the displacement field by adding time points.The response displacement field can be obtained by solving linear equations.

A computational method is proposed on the basis of controling partial differential equation of thin circular plate.It takes differential quadrature method in space domain and series in time domain,adopts DQ linear equations for solving all parameters of the displacement field by adding time points.

A numerical method is presented for the two dimensional quasi steady state heat transfer on high power density laser welding processes according to the keyhole model.The mathematic model is estabilished on the basis of the conservation of mass,momentum and energy.Computation has been performed in the curvilinear coordinate system by using the finite volume method.A position predict correct procedure was developed to accurately identify the solid liquid interface location during welding.Numerical example is on the study of a typical keyhold welding process of an AISI304 Stainless Steel plate.

The isograms of scalar Green's function in EM theory near singularity are discussed,including several bounded and unbounded 2-D and 3-D Green's function.The result shows that near singularity,the isogram of 2-D Green's function trends to circle,and 3-D Green's function trends to sphere regardless of the type of boundary.Whatever complex the bounded Green's function is,they have all same properties with unbounded Green's function.This is very useful to regularity process of integrative equation in EM field calaculation.

The Semi-analytical method is derived based on convolution-type varicational principles to solve the 2-D transient heat transfer problems,which takes finite element discretization in space domain and analytic function in time domain.

A semi-analytical method is derived on the basis of Gurtin variational principle for solving one dimension initial-value problems of dynamics under alternating forces. This method takes finite element discretization in space domain and series in time domain.

The two-dimensional molecular dynamics calculation is used to simulate ejection and damage phenomena. The intermolecular force is described by Morse potential. Molecules are initially located in equilibrium position and spaced so that the free surface has an angle shape for simulating real machined surface. Shock wave may be produced by motion of first layer of molecules (piston) or by impact of flyer of molecules. When the disturbance arrives at free surface, the boundary molecules start to run away from it with large velocity and the inside damage begins. The ratio of ejection velocity to the surface one changes from 1 to 3 and it is dependent on the shock strenth, surface angle and material property. When the semiangle is bigger than 60°, the boundary molecules can not run away from others, i.e. the ejection disappears. It also disappears when shock strength is lower than a limit value dependent ont he surface angle and material. In the both ejection and jetless cases the calculation shows the process of microvoid formation and growth.

The propagation of shock wave and it's reflection at free surface in two-dimensional lattice are considered and calculated by method of molecular dynamics. This lattice simulates the (1,0,0) plane for face centered cubic (f.c.c) or the (1,1,0)plane for body centered cubic(b.c.c).In the range of our calculation (u_p=10-75×10⁴cm/sec), the oscillation of particle velocity is'nt decrescent. The shock wave velocity is a linear function of average particle velocity. After reflection, the average particle velocity near free surface is equal to twice the piston velocity approximately, which agrees with macroscopic phenomena. The particles at outer-most layer of free surface, get the large value of velocity and go away from this surface. It is also similar to the macroscopic phenomena of ejection. At the later stage of expansion, the particles in the interial region may lose connection between them, that corresponds to the microscopic fracture.

A 15-fold integral over 5 momentum vectors which appears in nuclear matter theory and is subjected to the Pauli principle is discussed. The 15-fold integral is reduced to a 5-fold one due to the energy and momentum conservation and by choosing proper integration variables and the coordinate system. The number theory mesh method is used in the numerical calculations. The calculated results are given in tabular form for very wide range.